# 1.17.1 Multiplication (non-Calc)

#### (Non-calculator) multiplication – why so many methods?

• Different methods work for different people, and some are better depending on the size of number you are dealing with
• We recommend the following 3 methods depending on the size of number you are dealing with
(If in doubt all methods will work for all numbers!)

#### 1. Lattice method

(Best for numbers with two or more digits)

• This method allows you to work with digits
• So in the number 3 516 you would only need to work with the digits 3, 5, 1 and 6
• So if you can multiply up to 9×9 you can’t go wrong! So, 3516 × 23 = 80 868

#### 2. Partition method

(Best when one number has just one digit)

• This method keeps the value of the larger number intact
• So with 3 516 you would use 3000, 500, 10 and 6
• This method is not suitable for two larger numbers as you can end up with a lot of zero digits that are hard to keep track of  So, 3516 × 7 = 24 612

(Best for smaller, simpler cases)

• You may have seen this called ‘chunking’
• It is a way of building up to the answer using simple multiplication facts that can be worked out easily

eg. 13 × 23
1 × 23 = 23
2 × 23 = 46
4 × 23 = 92
8 × 23 =184

So, 13 × 23 = 1 × 23 + 4 × 23 + 8 × 23 = 23 + 92 + 184 = 299

#### Decimals

• These 3 methods can easily be adapted for use with decimal numbers
• You ignore the decimal point whilst multiplying but put it back in the correct place in order to reach a final answer

eg. 1.3 × 2.3
Ignoring the decimals this is 13 × 23, which from above is 299
There are two decimal places in total in the question, so there will be two decimal places in the answer

So, 1.3 × 2.3 = 2.99

#### Exam Tip

If you do forget your times tables then in the exam write a list out of the table you need as you do a question.

So for example, if you need to multiply by 8, and you’ve forgotten your 8 times tables, write it down: 8, 16, 24, 32, 40, 48, etc. as far as you need to.

### Worked Example

1. Multiply 2879 by 36

• As you have a 4-digit number multiplied by a 2-digit number then the lattice method (1) is the best choice • Notice the use of listing the 8 times table at the bottom to help with any you may have forgotten
2879 × 36 = 103 644
• Note that the method would still work if you had set it up as a 2×4 grid

2. Pencils are sold in boxes. Each box costs £1.25 and each box contains 15 pencils.

Tyler buys 35 boxes of pencils.

(a) Work out how many pencils Tyler has in total.

(b) Work out the total cost for all the boxes Tyler buys.

(a)

This is a roundabout way of asking you to work out 15×35
As this is a simpl-ish case (3) you should use the repeated addition method

1 × 35 = 35
2 × 35 = 70
4 × 35 = 140
8 × 35 = 280
16 × 35 = 560

It doesn’t matter if you go past 15 …

15 × 35 = 16 × 35 – 1 × 35 = 560 – 35
15 × 35 = 525

(b)

This question is 1.25×35 so involves decimals (4)
Ignoring the decimals it becomes 125×35 and so the lattice method is best 125 × 35 = 4375

Now count the decimal places from the question and put the decimal point back in the correct place

£1.25 × 35 = £43.75

#### Exam Tip

Okay, getting the highlighter out during an exam may be a touch excessive! But do use your grid/diagram to help you answer the question – the highlighter in the example above makes it clear which digits to add up at each stage.  You can do this in pen or pencil but do make sure you can still read the digits underneath as it is all part of your method/working.

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